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arXiv · 2608.00802

Counterexamples to the Landis conjecture in dimensions three and higher

Rupert L. Frank·Paata Ivanisvili
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Abstract

In every dimension three and higher we construct a nonzero function that satisfies the stationary Schr\"odinger equation with bounded, real-valued potential and decays like $\exp(-c|x|^{4/3})$. This gives a counterexample to the Landis conjecture in dimension three and higher.

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Rupert L. Frank, Paata Ivanisvili. 2026-08-01. Counterexamples to the Landis conjecture in dimensions three and higher. https://arxiv.org/abs/2608.00802

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